Question

Hello, I need some assistance with this precalculus homework question, please?HW Q4

Answer 1

Step 1. The information that we have is:

The principal amount of the investment P:

P=500

The interest rate r:

r=12%

The time of the investment t in years:

t=2

And we also know that the investment is compounded quarterly.

Step 2. We will need the interest rate as a decimal number, for this, we divide it by 100:

$\begin{gathered} r=12/100 \\ r=0.12 \end{gathered}$

We will also need n, which is the number of times of compounding over a year. Since it is compounded quarterly, it is compounded 4 times per year, therefore, the value of n will be 4:

$n=4$

Step 3. Using the compound interest formula

$A=P(1+\frac{r}{n})^{nt}$

Where A is the final amount.

Step 4. Substituting the known values into the formula:

$A=500(1+\frac{0.12}{4})^{4\times2}$

Step 5. The final step is to solve the operations.

First, we simplify the exponent:

$A=500(1+\frac{0.12}{4})^8$

Then, we make the division:

$A=500(1+0.03)^8$

Add 1 and 0.03:

$A=500(1.03)^8$

Keep solving the rest of the operations to find the final amount (the result of the investment after 2 years):

$\begin{gathered} A=500(1.03)^{8} \\ A=500(1.26677) \\ A=633.385 \end{gathered}$

Rounding the result to the nearest cent:

$A=633.39$

The final amount is $633.39

Answer: 633.39